First, we must assume that the statement is correct for some positive integer n. That is, is assumed to be correct.

According to the principle of induction, it will be correct for all positive integers if we prove that, given the assumption that it is correct for some positive integer n, it is also correct for n+1. That is to say, we now need to prove that the following equation:

(*)

Holds.

However, from the assumption we have, we know that

So we can substitute this expression from the LHS of (*), and then we get:

as the LHS.
The RHS of (*) stays . Now we need to prove both sides are equal. Let's play with the left hand side:

So the LHS of (*) is equal to . But so is the RHS, so we conclude that (*) holds and therefore the equation is correct.